Electroweak vacuum stability and the seesaw mechanism revisited

We study the electroweak vacuum stability in Type I seesaw models for three generations of neutrinos in scenarios where the right-handed neutrinos have explicit bare mass terms in the Lagrangian and where these are dynamically generated through the mechanism of spontaneous symmetry breaking. To best highlight the difference of the two cases we concentrate on the absolute stability of the scalar potential. We observe that for the first scenario, the scale at which the scalar potential becomes unstable is lower from that within the standard model. In addition the Yukawa couplings $$\mathbf {Y}_\nu $$ are constrained such that $$\mathrm {Tr}{[\mathbf {Y}^{\dagger }_\nu \mathbf {Y}_{\nu }}] \lesssim 10^{-3}$$. In the second scenario the electroweak stability can be improved in a large region of parameter space. However, we found that the scalar used to break the lepton number symmetry cannot be too light and have a large coupling to right-handed neutrinos in order for the seesaw mechanism to be a valid mechanism for neutrino mass generation. In this case we have $$\mathrm {Tr}[\mathbf {Y}^\dagger _{\nu } \mathbf {Y}_\nu ]\lesssim 0.01$$